Your computations are correct. The fundamental difficulty is that one cannot generally expect more than a couple of places of accuracy from a normal approximation to a Poisson distribution. For your problem, it may be best to look at the complementary probabilities in the right tail. > 1-ppois(687, 625) [1] 0.006821267 > 1-pnorm(687.5, 625, 25) [1] 0.006209665 > 1-pnorm(687, 625, 25) [1] 0.006569119 From close inspection of the plot below, one can see that the normal approximation already slightly underestimates the right-tail probability. The continuity correction takes away a little probability from that tail, which in this case happens to make it even worse. [![enter image description here][1]][1] The continuity correction usually improves the approximation, but that may be true only when the approximation is _already very good._ In your problem the approximation is not good enough for a discussion of the third and fourth decimal places to be productive. [1]: https://i.sstatic.net/Im4G5.png